Pattern generation by dissipative parametric instability
Nonlinear instabilities are responsible for spontaneous pattern formation in a vast number of natural and engineered systems ranging from biology to galaxies build-up. We propose a new instability mechanism leading to pattern formation in spatially extended nonlinear systems based on a periodic anti...
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| Veröffentlicht in: | arXiv.org 2015-12 |
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| creator | Perego, A M Tarasov, N Churkin, D V Turitsyn, S K Staliunas, K |
| description | Nonlinear instabilities are responsible for spontaneous pattern formation in a vast number of natural and engineered systems ranging from biology to galaxies build-up. We propose a new instability mechanism leading to pattern formation in spatially extended nonlinear systems based on a periodic antiphase modulation of spectrally-dependent losses arranged in a zig-zag way: an effective filtering is imposed at symmetrically located wavenumbers k and -k in alternating order. The properties of the dissipative parametric instability differ from the features of the both key classical concepts of modulation instabilities: the Benjamin-Feir, and the Faraday instability. We demonstrate how dissipative parametric instability can lead to the formation of stable patterns in one and two-dimensional systems. The proposed instability mechanism is generic and can naturally occur or can be implemented in various physical systems. |
| doi_str_mv | 10.48550/arxiv.1512.03482 |
| format | Article |
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We propose a new instability mechanism leading to pattern formation in spatially extended nonlinear systems based on a periodic antiphase modulation of spectrally-dependent losses arranged in a zig-zag way: an effective filtering is imposed at symmetrically located wavenumbers k and -k in alternating order. The properties of the dissipative parametric instability differ from the features of the both key classical concepts of modulation instabilities: the Benjamin-Feir, and the Faraday instability. We demonstrate how dissipative parametric instability can lead to the formation of stable patterns in one and two-dimensional systems. 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| subjects | Dimensional stability Galaxies Modulation Nonlinear systems Pattern generation Physics - Pattern Formation and Solitons Stability |
| title | Pattern generation by dissipative parametric instability |
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